Triangle Calculator
Area: -
Perimeter: -
Heights: -
Classification: -
Understanding Triangles
What is a Triangle?
A triangle is a polygon with three sides and three angles. Key elements include:
- Three sides and three angles
- Sum of angles = 180°
- Area formulas (multiple methods)
- Triangle inequality theorem
- Congruence conditions
- Similarity properties
- Special triangles (30-60-90, 45-45-90)
- Medians and centroids
- Altitudes and orthocenter
- Angle bisectors and incenter
- Perpendicular bisectors and circumcenter
Key Formulas
Area Formulas:
A = ½bh (base × height)
A = ½ab×sin(C) (two sides and included angle)
A = √(s(s-a)(s-b)(s-c)) (Heron's formula)
Perimeter:
P = a + b + c
Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines:
c² = a² + b² - 2ab×cos(C)
Triangle Classifications
By Angles
- Acute (all angles < 90°)
- Right (one angle = 90°)
- Obtuse (one angle > 90°)
- Equiangular (all angles = 60°)
By Sides
- Scalene (all sides different)
- Isosceles (two sides equal)
- Equilateral (all sides equal)
Advanced Concepts
Centers of Triangle
- Centroid (medians)
- Orthocenter (altitudes)
- Incenter (angle bisectors)
- Circumcenter (perpendicular bisectors)
- Euler line relationships
Special Lines
- Medians
- Altitudes
- Angle bisectors
- Perpendicular bisectors
- Symmedians
Real-World Applications
Engineering
- Structural design
- Surveying
- Navigation
- Force analysis
Architecture
- Roof design
- Bridge construction
- Support structures
- Space planning
Science
- Physics calculations
- Astronomy
- Optics
- Crystallography